Question

Solve for x: `(3x^2 + 5x + 18)/(5x^2 + 6x + 12) = (3x + 5)/(5x - 6)`.

Answer 1

Multiplying the Numerator and Denominator of R.H.S. by -x
`(3x^2 + 5x + 18)/(5x^2 + 6x + 12) = (-3x^2 + 5)/(-5x^2 - 6)`
Since, each ratio = `"Sum of antecedents"/"Sum of consequents"`
so `(3x^2 + 5x + 18 - 3x^2 - 5x)/(5x^2 + 6x + 12 - 5x^2 - 6x)`
= `(-3x^2 - 5x)/(-5x^2 - 6x)`
`(18)/(12) = (-3x^2 - 5x)/(-5x^2 - 6x)`
⇒ `(3)/(2) = (-3x^2 - 5x)/(-5x^2 - 6x)`
⇒ `(3)/(2) = (3x + 5)/(5x + 6)`
⇒ 15x + 18 = +x + 10
⇒ 9x = -8
⇒ x = `(-8)/(9).`